Colorful Stick Algebra

Step Five to Games of Thing:
Colorful Stick Algebra

In my last blog I show you the possibility of formulating the Boolean algebra as T Algebra. But due to the complexity of it to represent expressions containing a sequence of ORs we have to think about creating a simple algebra of pictures. To overcome such difficulties we can develop sticks algebra.

Stick Arithmetics

 TRUE is represented by

and FALSE is represented by VOID or

The two axioms of the arithmetic of logic is the cancelation law dan the condensation law.

The Law of Cancelation [[ ]] =     is represented by

The Law of Condensation [ ] [ ] = [ ] is represented by

Sticks Algebra

NOT a is drawn as

 

a OR b is drawn as

NOT (a OR b) is drawn as

The axioms of Brownian Cross algebra are Position and Transposition.

The Law of position [[a]a]=  in stick algebra is

Law of transposition [[ac][bc]]=[[a][b]]c

Simplifying Sticks Algebra

The axiom pair can be replaced by single axiom the  Huntington Axiom as it is used by Louis Kauffman in his box algebra.    The Huntington Axiom [[a][b]][[a]b]=a  can be drawn as

Last remarks 

The colorful V Algebra, colorful T algebra and the colorful Stick algebra can be perceived as a solitary games of arrangement and disposal of colored objects. Seeing the algebras as games, make me think about the possibility of creating the algebra of things as the formulation of Boolean algebra of objects  in 3 dimensional space. One of such things algebra will be discussed in my next blog: the Cards Algebra